Question

Icrophones are often preferred for the r Ition (3x^(2)+3y^(2)-9y)^(2)=81x^(2)+81y^(2)

Answer 1

The equation (3x^(2)+3y^(2)-9y)^(2) = 81x^(2) + 81y^(2) can be simplified as follows:

First, we can expand the left-hand side of the equation using the square of a binomial formula:

(3x^(2) + 3y^(2) - 9y)^(2) = (3x^(2))^2 + 2(3x^(2))(3y^(2) - 9y) + (3y^(2) - 9y)^2

= 9x^(4) + 54x^(2)y^(2) - 54x^(2)y + 9y^(4) - 54y^(3) + 81y^(2)

Next, we can simplify the right-hand side of the equation:

81x^(2) + 81y^(2) = 81(x^(2) + y^(2))

Now we can substitute the simplified right-hand side into the left-hand side:

9x^(4) + 54x^(2)y^(2) - 54x^(2)y + 9y^(4) - 54y^(3) + 81y^(2) = 81(x^(2) + y^(2))

This equation can be further simplified by dividing both sides by 9:

x^(4) + 6x^(2)y^(2) - 6x^(2)y + y^(4) - 6y^(3) + 9y^(2) = 9(x^(2) + y^(2))

Therefore, the simplified form of the equation (3x^(2)+3y^(2)-9y)^(2) = 81x^(2) + 81y^(2) is x^(4) + 6x^(2)y^(2) - 6x^(2)y + y^(4) - 6y^(3) + 9y^(2) = 9(x^(2) + y^(2)).